Q32 of 45 Page 12

Find the area of the shaded region in Fig. 2, where arcs are drawn with centres A, B, C and D intersect in pairs at mid - points P, Q, R and S of the sides AB, BC, CD and DA respectively of a square ABCD of side 12 cm. [Use π = 3.14]

(CBSE 2018)


Given:


• Square ABCD with side 12 cm


• 4 quarter circles on each of the four vertices, each with a radius(r) 6 cm


Required Area = Ar(PQRS)


(area enclosed within red arcs)


= Area of Square ABCD – Area of Four quarter circles


= Area of Square(side 12cm) – Area of a full circle (radius 6cm)


= (12×12) – π(6)2


(Area of Square = (Side)2 ; Area of Circle = πr2)


= 144 – 3.14(36)


= 113.04 cm2

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